Despite the continuing attacks, the violence is still far below that seen before or during Israel's three-week offensive in the Palestinian territory. Egyptian mediators are seeking a long-term truce; on Tuesday Hamas offered a one-year cease-fire.

A Grad rocket exploded Tuesday morning in Ashkelon, an Israeli city of 122,000 people on the Mediterranean coast about 10 miles (16 kilometers) north of Gaza. The blast damaged vehicles and buildings, but no one was hurt.

It was the first time Gaza militants had fired a Grad since Israel's offensive ended Jan. 17. Other rockets fired since then have been smaller, homemade versions.

Israel hit back at nightfall. Warplanes blasted the 8-mile (14-kilometer) Gaza-Egypt border after warning residents to leave — alerts that have become routine preceding almost daily airstrikes on the tunnels. The Israeli military said the planes hit five tunnels, a rocket-launching site and a Hamas outpost. No casualties were reported.

Despite flare-ups in the two weeks since Israel and Hamas decided separately on a truce, both sides have a clear interest in keeping a lid on violence.

Israel has an election in a week, and another full-scale conflict could harm the chances of moderate candidates from parties now in the government, further boosting the hawkish front-runner, former Prime Minister Benjamin Netanyahu.

Hamas badly needs an accord that would reopen Gaza border crossings with Israel and Egypt to relieve the severe shortages that plague the 1.4 million people in the impoverished territory. A blockade was imposed when Hamas violently seized power in June 2007, because Israel considers Hamas a terrorist group and Egypt fears the influence of Islamic extremists.

Egypt is mediating indirect truce negotiations; Israel and Hamas refuse to talk face to face.

Diplomatic activity spanned the Middle East. As a Hamas delegation met with Egyptian officials, Khaled Mashaal, the exiled Hamas leader, was in Iran for talks. Foreign ministers of pro-Western Arab countries gathered in Abu Dhabi and pushed Hamas to agree to a truce by Thursday.

During the Israeli offensive last month, militants fired hundreds of rockets at Israel, including Grads that struck Ashkelon and cities farther from Gaza. Israeli planes, tanks, artillery and troops pulverized hundreds of Gaza government buildings, police stations and apartment buildings, killing 1,300 people, according to Palestinian figures.

The level of violence has dropped considerably since then, and Tuesday's exchange might be among the last shots before a truce deal.

Hamas officials said they were offering a one-year cease-fire in exchange for opening the borders. Israel was inclined to agree but insisted that Hamas arms smuggling must be stopped.

Israeli Defense Minister Ehud Barak described the steady trickle of rocket fire from Gaza as political posturing.

"As after every successful operation, there are still some final spasms and effort by the enemy to attack and be the last to fire rockets and give the false impression that they weren't hit as hard as they were in reality," he said at a security conference.

Earlier Barak said Israel would respond to quiet from Gaza with quiet of its own. But, he added, "if it is necessary to deal another, even stronger, blow, then at the right time and in the right way, an additional and stronger blow will be dealt."

Barak and Foreign Minister Tzipi Livni are running for prime minister of Israel on Feb. 10. Livni also has threatened to hit Hamas again, but Netanyahu has gone further, advocating forcible removal of the militant group from power in Gaza.

Inspecting the site of the rocket attack in Ashkelon, Netanyahu turned that into a pledge. "A government led by me will topple the Hamas government in Gaza and bring peace and security to the south (of Israel)," he said.

The latest polls say Netanyahu's Likud Party and its hawkish allies are poised to win a majority in parliament, paving the way for him to become premier.

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Associated Press writers Barbara Surk in Abu Dhabi and Ibrahim Barzak in Gaza City contributed to this report.